Is it possible to have true transparency (without ghost shadows)?
What is probably happening here is a "Z-fight" between the surface of the transparent wall and that of the opaque one, meaning that since they are overlapping exactly along one of their faces, the render engine is confused as to which one to use for shading calculations.

One may think that a fully white transparent surface wouldn't Z-fight, ...but it does.



As a solution: remove the overlap! Move the surface a tiny bit away (or inside) the opaque wall.